Category Archives: Vaguely “scientific” speculation

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I have a hypothesis that explains why in many (most?) species, males have a shorter life expectancy than females. My apologies if this has been thought of before, or if it’s already well-known. It’s quite likely that I’m re-inventing the wheel here, that I’ve come across the current explanation before somewhere, and have simply forgotten. I have a keen interest in evolutionary theory, but I’m not a biologist.

The hypothesis is this: males are subject to more exploitation by parasites than females, because in general parasites “want” their host species to thrive. Over the course of a lifetime, this greater exploitation takes its toll.

In non-monogamous species, males are useful for fertilizing the eggs of the females, but not much else. In effect, after donating sperm most of them are redundant. They use up the food supply that could otherwise swell numbers of individual members of the species, and hence safeguard the species itself. In non-monogamous species, too many males are “bad for the species”. Drone bees consume as much nectar as honey-producing females. Male elephant seals consume far more fish than their smaller female counterparts, and few of them even get to donate sperm.

Farmers — in effect, human parasites of animals used as food — know all this, and so they usually kill males apart from the few needed to fertilize females. In doing so, they strengthen the species they parasitize, in the sense of increasing their numbers and assuring their future. Through domestication, the humble jungle fowl of Asian forests has become the mighty chicken, found in huge numbers all over the world. Much the same applies to cattle and sheep, which now occupy much of the earth’s surface.

Most parasites (such as microbes) are brainless, but through the process of natural selection they adopt “strategies” which can promote their numbers. In most cases, these strategies ensure that their host species do well enough to function reliably as hosts. The parasites aren’t actually thinking as human farmers think, of course, but over many generations they stumble upon similar strategies, which become established as the parasites that benefit from them proliferate.

With sex ratios, the “interests” of species and genes conflict. What’s “good for the species” is a much larger proportion of females than males, at least in non-monogamous species. But what’s “good for the genes” is a roughly equal number of males and females (as explained by Fisher’s Principle). The fact that in most species the ratio of males to females is indeed 1:1 makes a compelling case for a gene-centered understanding of evolution (a la Richard Dawkins’ Selfish Gene), and against group selectionism.

This hypothesis (I hesitate to call it “my” hypothesis) should be easy enough to test, as it entails that there should be a greater difference in male–female life expectancy in non-monogamous species than in monogamous species. It also entails that many of the diseases we associate with early male mortality (such as coronary heart disease, possibly suicide) may in fact be partially caused by infection by microbes.

[This blog post was prompted by this Scitable discussion. Unfortunately comments were closed before I could contribute.]

Laws are bits of language that describe regularities in nature. If the laws are true, the regularities are real. Laws are general claims, but they are more than accidental generalisations such as “everyone in this room is over five feet tall”. Laws are more like hyper-generalisations in that they don’t just describe what has actually been the case so far — they describe what would be the case, even if the states of affairs that would make them true have not yet come to pass.

There aren’t any laws about the heights of people who happen to be in a room together, but we’d be moving in that direction if we arranged some sort of screening mechanism that only allowed admittance to that room on the basis of height. Genuinely scientific laws rely on such mechanisms when they describe such things as the electric charge of fermions in an atomic nucleus.

Many fundamental laws of physics like Pauli’s Exclusion Principle do not admit of exceptions. Exceptionless laws like that are quite common in physics and chemistry. What about biology?

The question whether there are laws in biology is too often understood as asking whether there are exceptionless laws in biology. I’d guess there probably aren’t any such laws, because the categories of biology (species, etc.) are not like the categories of physics.

But it does not follow that biology has no laws. The salient feature of laws is not that they admit of no exceptions but that the links they express (between categories, concepts, etc.) are non-accidental.

Examples: animals with high male parental investment tend to be monogamous; mammalian mothers tend to be protective of their young. The biological functions of parental investment and pair-bonding are linked; and so are the functions of producing milk and caring for young.

Those links entitle us to draw inferences: if we hear that animals of species X exhibit high male parental investment, we can guess that they are monogamous, although there is always the possibility that we are dealing with an exception. If we hear that Y is a female mammal, we can guess that she is protective of her young, even though there is always the possibility that this particular individual’s behaviour is “aberrant”.

I hope it’s clear that biology does critically rely on and describe non-accidental links between categories — links that entitle us to make inferences between claims containing the corresponding concepts. It is that warrant to infer that makes for genuine scientific laws, not their exceptionlessness.

Biological laws have exceptions because many biological categories are “functional” (as exemplified above). In describing, explaining, predicting (etc.) things biologically, we adopt what Dennett calls the “design stance”. We assume that things have functions (purposes, goals, tasks, etc.) and that they perform those functions more or less well “as they were designed” to. “Working properly” shades into “less-than-optimal performance”, which in turn shades into out-and-out “malfunction”. Thus biological categories have fuzzy edges, in other words, these categories have grey areas where there are exceptions.

(Warning: of course nothing in biology is literally designed by a designer. The main point of evolutionary theory is to show how no such design is required. Talk of design, purposes, goals etc. in biology is just shorthand for past contribution to survival and reproduction.)

Darwin’s theory of evolution generates almost as much suspicion today as it did when it first appeared in the nineteenth century.

The theory has two main components, and there are two corresponding sorts of unease about it. The first component is natural selection, in which organisms are shaped by environmental pressures. The second is sexual selection, in which organisms are shaped by the choices of potential sexual partners.

The first component of Darwin’s theory undermines the assumption of a cosmic designer, so the first sort of unease tends to be felt by people who have traditional religious beliefs. Notice, though, that natural selection doesn’t really undermine the looser idea that living things are shaped in an appropriate way for living in their environments. In a metaphorical sense they are “designed”, although they are not literally designed by a conscious or intelligent designer with a plan. The “watchmaker” is “blind”, in Dawkins’ metaphor, but he is still a bit like a watchmaker. Examples of convergent evolution (think of similarities between marsupial moles and placental moles) illustrate how environmental niches shape the living things that inhabit them: similar niches can shape their inhabitants in strikingly similar ways.

The second component of Darwin’s theory is quite different. If natural selection is all about “fitting in with the environment”, sexual selection is all about “standing out from the crowd”. Far from working towards a smoother or more economical fit between organism and environment, sexual selection introduces capricious extravagance. If natural selection makes for traits that are “sensible and practical”, sexual selection makes for traits that are “crazy and impractical”.

With sexual selection comes ostentatious ornamentation, “runaway” emphasis on arbitrary traits, advertising, “handicapping” to subvert false advertising, prodigious waste, ritual, and romance, among other things. Ironically, as intelligence — or at least choice — is an essential part of sexual selection, it tends to introduce features that are “stupid” inasmuch as they are unsuited to the environment, and “irrational” inasmuch as they are harmful to the individuals who have them. (So much for the nearest thing nature has to “intelligent designl”!) Some specific traits (such as the Irish elk’s gigantic antlers) no doubt contribute to the extinction of the entire species.

Darwin used the word ‘man’ (meaning mankind) in the title of his main work on sexual selection, because he recognised its importance for understanding the evolution of our own species. The idiosyncrasies of human behaviour, culture and art are more complicated than those of bower birds, but they are similar in that their main engine is usually sexual selection. We too should recognise its importance, and the relevance of evolutionary theory for our self-understanding as humans.

In the nineteenth century, delicate sensibilities and Victorian piety were offended by Darwinism. In the present day, delicate sensibilities and twenty-first century piety are still offended. Our pieties are moral rather than religious, and take the form of strong distastes for beliefs that can be construed as misogynistic, sexist, racist, or homophobic. Such beliefs as that men and women have innately different intellectual strengths, say, or that rape can be explained from an evolutionary perspective, say, are frowned upon in our day as much as atheism was in Darwin’s day. The hierarchical institutions which discourage such thoughts are no longer those of the church, but of academia.

But that is all wrong. Rather than yielding to pressure to avoid offence, or promoting a dishonest political agenda, we should stop frowning upon “impious thoughts” and instead try to avoid immoral actions. Misogyny, sexism, homophobia and racism are best understood not as “having the wrong beliefs” but as willingness to behave in ways that disregard interests because of group-membership. They’re morally wrong, often extremely so, but not because of anything like impiety.

Many people take valid deductive arguments to be the guiding ideal or “paradigm” of evidence. There are two obvious reasons for this. The first is that in mathematics, the proof of a theorem is essentially a deductive argument, and mathematical proof is perhaps the closest thing we can have to certainty. The second is that when people try to persuade one another of something, they appeal to shared beliefs, which each hopes will imply something the other has no choice but to accept. This gives the shared beliefs the function of premises — and persuasion becomes the derivation of a conclusion from those premises.

Buoyed by the thought that proof and persuasion are achieved by arguments, we cast about in search of their equivalent in “empirical enquiry” — and inevitably arrive at induction. (By ‘induction’ I always mean enumerative induction: for example, the sighting of several white swans leads to the general claim that all swans are white.) An inductive “argument” with true “premises” doesn’t guarantee the truth of its “conclusion” as a valid deductive argument does, but it does lead to it with mechanical inevitability. It leaves no room for choice as to what its conclusion will be. No “guesswork” is involved — the “data” determine the resulting “theory”. The latter is “based on” the former in much the same way as the conclusion of a deductive argument is “based on” its premises.

The ubiquity of the thought that “evidence consists of arguments” is underlined by the widespread use of words like ‘basis’, ’grounds’, ‘foundations’, ‘support’, etc. — as if these words were synonymous with ‘evidence’.

There’s a remarkable fact about arguments, which can be loosely expressed as follows: “the conclusion doesn’t tell us anything genuinely new — it just rearranges information already contained the premises”. That’s a loose way of putting it, because obviously theorems in mathematics can be surprising. But they’re mostly surprising because we don’t expect them to be able to say what they do say, given that they were derived from such meagre “input” as is contained in the axioms.

Theorems never “reach out” beyond what can be derived from the axioms. And the conclusion of an inductive argument only reaches out beyond what is contained in its premises inasmuch as it merely generalises from them. It can’t come up with new concepts. If we were limited to deduction and induction, we might be able to do logic and mathematics, and to generalise about what we can observe directly. But we wouldn’t be able to talk about the sort of things science talks about. In that sense, both deduction and induction are “closed” with respect to their “raw material”. Everything mentioned in their conclusions is internal to the system of axioms or beliefs expressed by their premises.

If we assume that evidence consists of arguments, it amounts to “being implied by what you know already”. It’s analogous to what can be got from a library that contains nothing but books you have already read. It’s an internal guarantee or assurance, the sort of thing that invites adjectives like “strong”, or possibly “overwhelming”.

But that sort of evidence doesn’t play a big role in science. Science isn’t trying to give us an internal sense of assurance, but to give us an understanding of external reality. In other words, it’s not aimed at justification but at truth. Unlike the best that can be achieved by deduction and induction, science “reaches out” beyond any system of axioms or beliefs working as premises. To achieve that, science simply cannot avoid guesswork. In embracing guesswork, scientific theory is not fully constrained by observation. In other words, theory is underdetermined by “data”. Typically, several possible theories are consistent with any given set of “data”.

A scientific theory is a representation of its subject matter. It can represent it by literally being true of it, or by modelling it. Hypotheses are true or false — they consist of symbols, some of which stand for real things. Models mimic the behaviour of some aspect of reality in some relevant respect. Either way, evidence in science consists of mere indications, often sporadic and peripheral, that the representations in question do in fact represent their subject matter faithfully or accurately. A theory is related to its subject matter in somewhat the same way as a map is related to its terrain. The image of map and terrain is appropriate — and the old image of conclusion and premises of an argument is inappropriate. The main purpose of observation in science is not to gather “data” to work as premises in an argument, but to check here and there to see whether the “map” and the “terrain” do in fact seem to fit.

Understood in this way, evidence is no longer a matter of proof or persuasion — of leaving no alternative to accepting a “conclusion” — but of seeking new indications that a representation is accurate. The most obvious such indications are passing tests and providing explanations. A theory passes a test when it predicts something that can be observed, and new observation confirms the prediction. A theory explains successfully when it newly encompasses something formerly baffling. Both involve seeking new facts rather than mechanically deriving something from old facts.

Science is more a process of discovery rather than of justification, and scientific evidence is more like what an explorer can bring to light through travel than what a scholar can demonstrate in his study.

Replication of exactly the same test is epistemically worthless. Only by varying the conditions in which a test is done do we set up more “hurdles” for a hypothesis to “fall” at or “make it over”. In effect, varying conditions is a way of doing more tests. But inasmuch as any individual test gives us an independent reason to think a hypothesis is true, it differs from all of the other tests the hypothesis passes, and so it isn’t an exact repeat performance or perfect replication of any other test.

Of course we insist that test results should be reliable and objective. So we insist that they be inter-subjectively checkable, that they can in principle be done by different people, in different places, at different times.

The point of replicability is to prevent fraud or reliance on mere testimony. It’s not to provide many instances for an inductive generalisation to be based on. Even if science relied on induction like that — and I would argue that no genuine science does — perfectly exact replication would be of no use. For example, consider the inductive generalisation “all swans are white”. That would have to be based on several sightings of several white swans rather than the same single white swan. So even here, each individual sighting would have to differ from all of the others, at least insofar as it is the sighting of a different swan.

Species with high male parental investment use a reproductive “strategy” in which bringing offspring to viable adulthood normally depends on support from both parents. Why “normally”? – A single parent might get lucky and manage it in times of abundance, but even then, the resulting adult will have to compete against other adults who have enjoyed the attentions of both parents. That will usually be a disadvantage. We know it must usually be a disadvantage, because if it were not, the alternative one-parent strategy would spread throughout the population and become the norm. A male who is absent for the rearing of offspring can wander off and father other offspring. A female who does not need a male partner to rear offspring can choose from a wider variety of males, some of which will be of higher quality than others. This is what does happen with many animals such as grazing ruminants, and it happens because – given the specific needs of their young – that is a more efficient way of producing viable adults.

Please note that although different species use different reproductive strategies, it is wrong to suppose that there are smooth gradations between them. The most successful strategy will always spread throughout the population and become established as the norm. Some species simply lay eggs and leave the young to fend for themselves. In other species, mothers play a special role as parent. In monogamous species, both parents play a role like the role of mothers. Their parental investment will be roughly equal, because their “biological interest” in reproducing is the same. Which strategy becomes established as the norm is determined by which is the most efficient method of producing viable adults in the next generation. But there can be little or no crossing over between these different strategies.

In species whose males do not wander off, sticking around to help provision the offspring isn’t just an added luxury for the female. It’s a matter of life and death for the offspring, and thus a matter of reproductive success or failure for both male and female. Since proliferation of genes in future generations is evolution’s “prime directive”, it’s a matter whose importance equals that of life and death for everyone involved. The male isn’t simply doing the female a favor – he’s using her to reproduce, just as she’s using him to reproduce.

When provisioning is a matter of life and death like that, a male who misspends his provisioning powers on another male’s offspring is in effect throwing away his ability to reproduce. And a female whose male squanders his provisioning powers on another female’s offspring in effect has her ability to reproduce stolen. Given evolution’s “prime directive”, these possibilities are bad news for one or other of them. Furthermore, the strategy of sharing provisioning between male and female opens up such possibilities. Monogamy and betrayal are two sides of the same biological coin.

So in species where male parental investment is high, something new enters the picture: potential parents of each sex set “terms and conditions” for each other in a partnership whose “purpose” is to bring offspring to viable adulthood. Each demands guarantees of fidelity from their partner (at the same time as being rather more relaxed about their own fidelity).

Whatever we choose to call this set of attachments and demands, it is close to the everyday folk psychological concept of love. It isn’t a selfless or sexless ideal, or an experienced “feeling”, but a real attachment between two members of a pair which serves a vital biological function. It involves possessiveness, jealousy, and the ever-present possibility of betrayal. In real life there are many variations on the theme of two parents exclusively attached to each other, of course, but I would argue that most of them involve some degree of betrayal of one sex by the other, even if those involved bite the bullet and observe the social decorum of calling it something more polite.

You might think this is a rather bleak view of love that “lowers humans to the level of animals”. But I would urge you instead to think of it as raising some animals (such as birds) to the level of humans.

Prime numbers are those that are divisible only by themselves and by the number one. Now I dislike arithmetic, and my heart sinks whenever I hear the word ‘divisible’, because it suggests boring activities such as counting or doing “long division sums”.

But I enjoy working with text, and trying out clever things with “find” and “change to” in applications such as InDesign. So it was a real pleasure to learn recently that GREP can be used to find prime numbers. (GREP is InDesign’s implementation of “regular expressions” for matching text.) Grasping how it can do that also helps to throw light on the concept of a prime number. And it does so in an intuitive and simple way that does not involve doing arithmetic.

Imagine an old-fashioned pavement made out of a fixed number of rectangular paving slabs laid side by side. Imagine a child walking from one end of the pavement to the other. By “avoiding the cracks” between them, the child can always reach the last slab, whatever their number, by simply stepping from one slab to the next. But by jumping over alternate slabs (i.e. every second slab), the child might not be able to land on the last slab – it depends whether there is an even number of them. Likewise, by taking big leaps of three slabs at a time, our child will only be able to land on the last slab if their total number is a multiple of three. And so on.

I hope you can see how this might continue into larger and larger numbers. So imagine this going on, with our child taking larger and larger steps, possibly with the help of a pair of stilts. For example, if the pavement is 15 slabs in length, the fifteenth slab can be reached by taking five big leaps of three slabs each, or three even longer stilted strides of five slabs each.

Now here’s the really important thing about prime numbers: the last slab of a prime number of such slabs can only be reached by taking a single step over all of the slabs that precede it.

GREP can be used to find prime numbers, because a simple GREP expression can match non-prime numbers. It manages to do that by mimicking the behavior of a child stepping over multiple paving slabs as just described.

Let’s build up a GREP expression slowly to see how this works. By analogy with reaching all the way to the final slap of a pavement, we want our GREP expression to match an entire series of letters. Let’s choose any letter at random, such as capital M.

We should start off with the simplest of GREP expressions (for clarity, they have this dark red color): the single letter M will match any single instance of the letter M. If I have a long series of Ms (like this: MMMMMMMMM) the GREP expression M+ will match the whole series at once. That’s because the plus sign asks it to match one or more Ms, and by default GREP is “greedy” – it will match as much as it can, in this case the whole series. We can change that default behavior by adding a question mark. In isolation, M+? will match the same as M on its own.

What we want to build is a GREP expression that will mimic the behavior of a child skipping over whole paving slabs (plural) rather than one-by-one by simply stepping over the cracks between them. The expression MM+? works for that purpose, because it will match two or more instances of the letter M, at the same time as matching as little as possible thanks to the ? at its end. This gets really useful when combined with parentheses to make a “unit” (MM+?), and \1 to match whatever that unit matches (the number one is used here because it’s the “first unit” in the entire expression).

Bearing in mind what I have just said about the default “greediness” of GREP and the way it can be overridden with a question mark ?, consider the following expression:

(MM+?)\1+

This expression is nearly what we’re looking for, as it matches as much as can be matched by repeatedly re-using its smallest constituent parts, where the parts in question are anything bigger than single letters. To illustrate, consider this series of six Ms: MMMMMM.

The MM+? in parentheses matches the first two Ms in MMMMMM. It won’t match all of them because the ? tells it to match as little as possible, and it won’t match just one, because it must match at least two. So now \1 matches a pair of Ms. So \1+ matches as many pairs of Ms as it can, to try and match all six Ms. As it happens, just two further pairs are needed.

This is analogous to a child reaching the final slab of a pavement of six slabs by jumping over the first two slabs in one go, then repeating the same feat twice. Reaching the last of any even number of slabs involves the same procedure, repeating the initial jump as many times as may be necessary.

But now suppose we use the same expression to try to match nine Ms. Just repeating matching pairs won’t work this time, because nine isn’t a multiple of two. This is where GREP does something clever. It “backtracks” as soon as it has to give up on its initial attempt to match the whole series by repeating a matching pair. Next, it tries matching MM+? to three Ms instead of two. This is what it must do, if you think about it, since it is trying to match as little as possible with the part of the expression in parentheses, yet as much as possible with the entire expression. The default “greediness” of GREP remains the “prime directive”, and it might be able to match more by trying repeated triples rather than repeated pairs of matched letters. And in the case of nine letters, it turns out happily again, with \1+ matching two further triples.

This is analogous to a child reaching a ninth slab by leaping over three in one go at first, then repeating it two more times.

I hope it’s obvious how this continues. GREP will keep trying out larger and larger initial matches as long as it fails to match the entire series by repeating its initial match. With non-prime numbers of letters, it will eventually succeed. But with prime numbers, it will never arrive at an initial match whose repetition succeeds in matching the entire series. So prime numbers are those that GREP can’t match when searching in series of the same character (such as the letter M).

There are couple of loose ends to tie up. GREP needs to recognize the start and the end of such a series. We might tell it only to look within entire paragraphs, in which case we should put ^ at the start of the expression and $ at the end (this is a standard GREP convention). Or we might use spaces between series to mark them off from each other, and look for any character except spaces instead of the letter M. Using standard GREP code for “positive lookbehind” (?<= ), “positive lookahead” (?= ), and “anything but” [^ ] set to spaces, it ends up like this:

(?<= )([^ ][^ ]+?)\1+(?= )

The expression (?<= )([^ ][^ ]+?)\1+(?= ) matches any series of the same character whose length is non-prime, but it won’t match any whose length is prime. It’s a straightforward matter to apply this in InDesign or any equivalent application to find prime numbers. (Interested readers familiar with InDesign can download a simple Javascript that demonstrates the basic idea here.)

I have tested several scripts for generating and testing quite large prime numbers, and GREP works remarkably efficiently when put to this unintended purpose. In doing so, I have acquired a more intuitive grasp of what prime numbers are, and why they are part of nature. For example, 13-year cicadas and 17-year cicadas only have to compete against each other every 13 × 17 = 221 years, when they emerge in the same year. It is no accident that evolution stumbles upon prime numbers in this sort of situation.

I can see why we might we might call primes the “building blocks” of the counting numbers. Best of all, I haven’t had to do any arithmetic! Hate arithmetic!

I often think that those who say we face “climate change catastrophe” mustn’t really understand the most basic tenet of evolutionary theory: that life involves a struggle for existence.

Consider, for example, what the Sunday Times television guide says about tonight’s wildlife documentary on BBC2, The Polar Bear Family and Me: “polar bears are the world’s largest carnivores, but global warming is making it more and more difficult for them to find food”.

In fact, individual polar bears have always found it difficult to find food. Whenever less food was available, their numbers fell, as more of them succumbed to various causes of death. Most such causes have always been related to food shortage: diseases of malnutrition, exhaustion through having to travel long distances to find food, attacks by other hungry polar bears, even killing at the hands of human beings they wouldn’t have approached if they hadn’t been so hungry.

Whenever more food was available, their numbers rose – up to the point at which food was difficult to find again. That brings us right back to the situation described in the previous paragraph. Polar bear numbers are not decided by ancient “polar bear wisdom” with which they thoughtfully control their own numbers, nor is there a “delicate balance of nature” in the Arctic that perfectly suits polar bears. The issue is always settled the hard way – by food shortages and by death.

As Arctic ice melts, polar bear numbers may be rising or falling – and no one seems to know with much confidence which. Polar bears are good swimmers, and they get most of their food in the form of other swimming animals such as seals. It might be that more open water has the effect of increasing the availability of food – a situation that sustains larger numbers of polar bears. Or it might be that more open water allows more polar bear competitors into their “turf”, which help to use up the food supply. Or that less ice means fewer air-holes where seals can be caught. These are situations that sustain smaller numbers of polar bears. But fewer bears means fewer competitors for each individual bear, which makes finding food slightly less difficult. Which reverses things a bit. Via many swings and roundabouts of fortune, a sort of balance is struck. It isn’t a balance that arises through design, or anything like it. It’s a balance that results from the “chips falling where they may”.

Whichever way the chips may fall, the difficulty of finding food remains roughly the same. The degree of difficulty is always approximately a matter of life and death.

I’m not sure why so many climate alarmists seem to be unaware of this situation, which exists pretty much everywhere in nature. It might be that their area of specialization has nothing to do with evolution, which makes them no better qualified than any other layperson to guess the effects on life of a changing climate. Or it might be that the insight Darwin credited Malthus for bringing to his attention has been largely forgotten in today’s attitudes to “ecosystems”. These attitudes assume that there is something akin to design in nature, and suffering gets much worse when a supposed “way things were meant to be” is disrupted.

Wherever there’s life, there’s a struggle for existence. Whether sea levels rise or fall, whether ice caps retreat or advance, whether the climate warms or cools, whether the earth is beset by floods or droughts, even if everything stays exactly the same – living things have to battle against each other and their environment as a matter of life and death. There’s a lot of suffering in all that strife, and changes are just as likely to bring a little relief from that vast tapestry of suffering as to make it a little worse.

As a simple example of so-called “supervenience”, consider a container of gas at a given temperature. There are infinitely many possible molecular states for any given temperature, and statistically they are bound to differ. The one respect in which they will not differ is in their mean kinetic energy. It sounds strange to say that the property of the gas being at that temperature “supervenes” on the property of its molecules being in this or that state. I would call it downright misleading inasmuch as it suggests that phenomenological thermodynamics describes a different “realm” from that described by statistical mechanics.

In fact, phenomenological thermodynamics and statistical mechanics are just different theories, one of which reduces the other. The fact that they are actually inconsistent with one another is a stark reminder of the difference between them. Yet this remains a classic case of successful inter-theoretic reduction. Statistical mechanics is capable of mimicking phenomenological thermodynamics well enough to recreate Boyle’s Law and other laws of thermodynamics in statistical form. A part of statistical mechanics has the same taxonomy as phenomenological thermodynamics – a taxonomy represented by the tick marks on a thermometer. Rather than saying one property “supervenes” on another property – as if there were “levels of reality” – we should say that the taxonomic classes of two theories are identical. The smoothness of the inter-theoretic reduction between the theories entitles us to make such identity claims.

I use this example because it is not particularly mysterious. When we start talking about the “supervenience” of the mental on the physical, the (traditional, dualist) suggestion that there are two different “realms” is often overpowering.